Go back to Flu Mortality

Results for 1989-1990 epidemic “BFGS” method:

For the guess of parameters beta = 0.3, alpha = 0.2, N = 1377, and I0 = 1 on the simple data, we obtained

beta = 0.8660146 alpha = 0.3524617 Ne = 1376.5374677 I0 = 12.5766151

The covariance matrix was

            [,1]          [,2]         [,3]         [,4]

[1,] 0.0007816005 0.0007921763 -0.003843416 -0.007148974 [2,] 0.0007921763 0.0009343933 -0.002570028 -0.004529554 [3,] -0.0038434158 -0.0025700278 -0.376947741 0.167820724 [4,] -0.0071489738 -0.0045295541 0.167820724 0.335574456

The MLE was 3987.069

Here’s a plot of the model with the data (blue is the model and red is the data)

our_data_with_fitted_basic_sir_model_bfgs_.pdf

Results for 1989-1990 epidemic “SANN” method:

For the guess of parameters beta = 0.3, alpha = 0.2, N = 1377, and I0 = 1 on the simple data, we obtained

beta = 1.2186258 alpha = 0.6013314 Ne = 1374.6471388 I0 = 4.1282104

The covariance matrix was

           [,1]         [,2]        [,3]        [,4]

[1,] 0.007873159 0.008398466 6.481873 -0.01774405 [2,] 0.008398466 0.009289811 7.343885 -0.01281983 [3,] 6.481873413 7.343884715 7500.602219 -2.47489698 [4,] -0.017744053 -0.012819826 -2.474897 0.21600125

The MLE was 3961.758

Here’s a plot of the model with the data (blue is the model and red is the data)

our_data_with_fitted_basic_sir_model_sann_.pdf

Weston: The parameter values are not as close as I would have liked, however, the MLE of 3961.758 is only a little lower than the previous MLE of 3987.069 from the “BFGS” method. What do you think about the difference?